%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : LCL170-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Sep 7 12:42:03 PM UTC 2026
% Result : Unsatisfiable 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of clauses : 18 ( 11 unt; 0 nHn; 10 RR)
% Number of literals : 27 ( 12 equ; 10 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 5 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 28 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(axiom_1_3,axiom,
axiom(implies(A,or(B,A))) ).
cnf(implies_definition,axiom,
implies(X,Y) = or(not(X),Y) ).
cnf(rule_1,axiom,
( theorem(X)
| ~ axiom(X) ) ).
cnf(prove_this,negated_conjecture,
~ theorem(implies(q,implies(p,q))) ).
cnf(refute_0_0,plain,
( ~ axiom(implies(A,or(B,A)))
| theorem(implies(A,or(B,A))) ),
inference(subst,[],[rule_1:[bind(X,$fot(implies(A,or(B,A))))]]) ).
cnf(refute_0_1,plain,
theorem(implies(A,or(B,A))),
inference(resolve,[$cnf( axiom(implies(A,or(B,A))) )],[axiom_1_3,refute_0_0]) ).
cnf(refute_0_2,plain,
theorem(implies(A,or(not(X_11),A))),
inference(subst,[],[refute_0_1:[bind(B,$fot(not(X_11)))]]) ).
cnf(refute_0_3,plain,
implies(X_11,A) = or(not(X_11),A),
inference(subst,[],[implies_definition:[bind(X,$fot(X_11)),bind(Y,$fot(A))]]) ).
cnf(refute_0_4,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_5,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_6,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( implies(X_11,A) != or(not(X_11),A)
| or(not(X_11),A) = implies(X_11,A) ),
inference(subst,[],[refute_0_6:[bind(X0,$fot(implies(X_11,A))),bind(Y0,$fot(or(not(X_11),A)))]]) ).
cnf(refute_0_8,plain,
or(not(X_11),A) = implies(X_11,A),
inference(resolve,[$cnf( $equal(implies(X_11,A),or(not(X_11),A)) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
( or(not(X_11),A) != implies(X_11,A)
| ~ theorem(implies(A,or(not(X_11),A)))
| theorem(implies(A,implies(X_11,A))) ),
introduced(tautology,[equality,[$cnf( theorem(implies(A,or(not(X_11),A))) ),[0,1],$fot(implies(X_11,A))]]) ).
cnf(refute_0_10,plain,
( ~ theorem(implies(A,or(not(X_11),A)))
| theorem(implies(A,implies(X_11,A))) ),
inference(resolve,[$cnf( $equal(or(not(X_11),A),implies(X_11,A)) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
theorem(implies(A,implies(X_11,A))),
inference(resolve,[$cnf( theorem(implies(A,or(not(X_11),A))) )],[refute_0_2,refute_0_10]) ).
cnf(refute_0_12,plain,
theorem(implies(q,implies(p,q))),
inference(subst,[],[refute_0_11:[bind(A,$fot(q)),bind(X_11,$fot(p))]]) ).
cnf(refute_0_13,plain,
$false,
inference(resolve,[$cnf( theorem(implies(q,implies(p,q))) )],[refute_0_12,prove_this]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL170-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.03 % Command : metis --show proof --show saturation %s
% 0.09/0.35 % Computer : n029.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 5 22:57:10 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36
% 0.12/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36
%------------------------------------------------------------------------------